A local finance company quotes a one-year loan at an interest rate of 16 percent

Question

A local finance company quotes a one-year loan at an interest rate of 16 percent. So, if you borrow $33,000, the interest for the year will be $5,280. Because you must repay a total of $38,280 in one year, the finance company requires you to pay $38,280/12, or $3,190.00, per month over the next 12 months. What rate would legally have to be quoted? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).) Annual percentage rate % What is the effective annual rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).) Effective annual rate %

Explanation / Answer

Solution:

Calculation of Annual Percentage Rate & Effective Annual Rate:

To find the APR and EAR, we need to use the actual cash flows of the loan. In other words, the interest rate quoted in the problem is only relevant to determine the total interest under the terms given. The interest rate for the cash flows of the loan is:

PVA = 33,000 = 3,190 {(1 – [1 / (1 +r)]12) /r}

Again, we cannot solve this equation for r, so we need to solve this equation by trial and error. Then,

r = 2.3593%

So the APR is:

APR = 12(2.3593%)

= 28.3116% = 28.31%

And the EAR is:

EAR = (1.023593)12 – 1

= 1.32286 - 1

= 0.32286

= 32.29%

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